{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss vaule: -18.00\n",
      "Loss vaule: -14.40\n",
      "Loss vaule: -11.52\n",
      "Loss vaule: -9.22\n",
      "Loss vaule: -7.37\n",
      "Loss vaule: -5.90\n",
      "Loss vaule: -4.72\n",
      "Loss vaule: -3.77\n",
      "Loss vaule: -3.02\n",
      "Loss vaule: -2.42\n",
      "Loss vaule: -1.93\n",
      "Loss vaule: -1.55\n",
      "Loss vaule: -1.24\n",
      "Loss vaule: -0.99\n",
      "Loss vaule: -0.79\n",
      "Loss vaule: -0.63\n",
      "Loss vaule: -0.51\n",
      "Loss vaule: -0.41\n",
      "Loss vaule: -0.32\n",
      "Loss vaule: -0.26\n",
      "Loss vaule: -0.21\n",
      "Loss vaule: -0.17\n",
      "Loss vaule: -0.13\n",
      "Loss vaule: -0.11\n",
      "Loss vaule: -0.09\n",
      "Loss vaule: -0.07\n",
      "Loss vaule: -0.05\n",
      "Loss vaule: -0.04\n",
      "Loss vaule: -0.03\n",
      "Loss vaule: -0.03\n",
      "Loss vaule: -0.02\n",
      "Loss vaule: -0.02\n",
      "Loss vaule: -0.01\n",
      "Loss vaule: -0.01\n",
      "Loss vaule: -0.01\n",
      "Loss vaule: -0.01\n",
      "Loss vaule: -0.01\n",
      "Loss vaule: -0.00\n",
      "Loss vaule: -0.00\n",
      "Loss vaule: -0.00\n",
      "Loss vaule: -0.00\n",
      "Loss vaule: -0.00\n",
      "Loss vaule: -0.00\n",
      "Loss vaule: -0.00\n",
      "Loss vaule: -0.00\n",
      "Loss vaule: -0.00\n",
      "Loss vaule: -0.00\n",
      "Loss vaule: -0.00\n",
      "Loss vaule: -0.00\n",
      "Loss vaule: -0.00\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "\n",
    "def function():\n",
    "    gradient = 2 * xi\n",
    "    return gradient\n",
    "\n",
    "epoch = 50\n",
    "lr = 0.1\n",
    "xi = -18\n",
    "\n",
    "trajectory = []\n",
    "\n",
    "for i in range(epoch):\n",
    "    trajectory.append(xi)\n",
    "    print(f'Loss vaule: {xi:.2f}')\n",
    "    xi = xi - lr * function()\n",
    "\n",
    "x = np.arange(-20, 20, 0.1)\n",
    "y = x ** 2 + 1\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11])\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "\n",
    "print(torch.arange(12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 画出函数图像\n",
    "plt.plot(x, y)\n",
    "x_trajectory = np.array(trajectory)\n",
    "y_trajectory = x_trajectory ** 2 + 1\n",
    "\n",
    "plt.scatter(x_trajectory, y_trajectory, color=\"red\", label='Gradient Descent Steps')\n",
    "plt.title('Gradient Descent on $f(x) = x^2 + 1$')\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel('y')\n",
    "# tap标签\n",
    "plt.legend()\n",
    "# grid 网格背景\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
